Annals of Statistics
- Ann. Statist.
- Volume 22, Number 1 (1994), 238-270.
Statistical Estimation and Optimal Recovery
New formulas are given for the minimax linear risk in estimating a linear functional of an unknown object from indirect data contaminated with random Gaussian noise. The formulas cover a variety of loss functions and do not require the symmetry of the convex a priori class. It is shown that affine minimax rules are within a few percent of minimax even among nonlinear rules, for a variety of loss functions. It is also shown that difficulty of estimation is measured by the modulus of continuity of the functional to be estimated. The method of proof exposes a correspondence between minimax affine estimates in the statistical estimation problem and optimal algorithms in the theory of optimal recovery.
Ann. Statist., Volume 22, Number 1 (1994), 238-270.
First available in Project Euclid: 11 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62C20: Minimax procedures
Secondary: 62G07: Density estimation 41A25: Rate of convergence, degree of approximation 43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
Donoho, David L. Statistical Estimation and Optimal Recovery. Ann. Statist. 22 (1994), no. 1, 238--270. doi:10.1214/aos/1176325367. https://projecteuclid.org/euclid.aos/1176325367